The C = 1 Matrix Model Formulation of Two Dimensional Yang-Mills Theories

Details The C = 1 Matrix Model Formulation of Two Dimensional Yang-Mills Theories The C = 1 Matrix Model Formulation of Two Dimensional Yang-Mills Theories

1993-07-28

arxiv.org/abs/hep-th/9307173v1

Mod. Phys. Lett. A8 (1993) 3201-3214

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, plain latex, DFTT 36/93

Scientific paper

We find the exact matrix model description of two dimensional Yang-Mills theories on a cylinder or on a torus and with an arbitrary compact gauge group. This matrix model is the singlet sector of a $c =1$ matrix model where the matrix field is in the fundamental representation of the gauge group. We also prove that the basic constituents of the theory are Sutherland fermions in the zero coupling limit, and this leads to an interesting connection between two dimensional gauge theories and one dimensional integrable systems. In particular we derive for all the classical groups the exact grand canonical partition function of the free fermion system corresponding to a two dimensional gauge theory on a torus.

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